LCM of 3, 5 and 15
2026-02-28 11:08 Diff
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Last updated on August 5, 2025

The Least Common Multiple (LCM) is the smallest number that when we divide by two or more numbers at a time, all three or more numbers divide into it. LCM also helps in math problems and everyday things like event planning or buying supplies. We will find the LCM of 3, 5 and 15 together and what that really means

What Is The LCM Of 3, 5 And 15?

The LCM or the least common multiple of 2 numbers is the smallest number that appears as a multiple of both numbers. In case of 3, 5 and 15, The LCM is 15. But how did we get to this answer? There are different ways to obtain a LCM of 2 or more numbers. Let us take a look at those methods.
 

How To Find The LCM Of 3, 5 And 15

Remember that we previously said there are plenty of ways to calculate the LCM of two numbers or more. Then some of those methods make it extremely easy for us to find the LCM of any two numbers. Those methods are: 

  • Listing of Multiples
  • Prime Factorization
  • Division Method

Finally, now we will learn how each of these methods can help us to calculate LCM of given numbers.
 

Finding LCM Of 3, 5 And 15 By Listing Of Multiples

This method will help us find the LCM of the numbers by listing the multiples of the given numbers. Let us take a step by step look at this method.


step 1: list all the multiples of the given numbers.


Multiples Of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27 and 30.


Multiples Of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45 and 50.


Multiple Of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135 and 150.


step 2: find the smallest common multiples in both the numbers. In this case, that number is 15 as highlighted above.


By this way we will be able to tell the LCM of given numbers.
 

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Finding The LCM By Prime Factorization

Let us break down the process of prime factorization into steps and make it easy for children to understand.
The first step is to break down the given numbers into its primal form. The primal form of the number is:


3= 3


5= 5


15= 5×3


As 5 and 3 are common, it will be considered only once. We will get the equation as (5×3)


So after the multiplication, we will be getting the LCM as 15.


As you can see, using this method can be easier for larger numbers compared to the previous method. 
 

Finding The LCM By Division Method

The method to calculate the LCM is really simple. We’ll break these given numbers apart till it comes down to one, by dividing it by the prime factors. The product of the divisors that will come is the LCM of the given numbers.


Let us understand it step by step:


The first thing is to find the number common in both the numbers. Here it is 3. In that case, we divide the numbers by 3. It will reduce the values of the numbers to 1, 5 and 5.


As 5 is a prime number, it can be divided by themselves. After this step, all the numbers in the last row will be 1.


This is the end of division. However, we will now find the product of the numbers on the left. The numbers on the left side are: 3 and 5. 


These numbers multiplied give 15. On this basis, therefore, the LCM of the 3, 5 And 15 becomes 15.
 

Common Mistakes That Are Made And How To Avoid Them For LCM Of 3, 5 And 15.

Let us look at some of the common mistakes that can happen while solving a given assignment regarding LCM.

Problem 1

If you have bags of candies: 3, 5, and 15 candies each, how many total candies to distribute equally?

Okay, lets begin


You have 15 candies. You can share them equally among different bags, making sure each bag has the same number of candies for everyone.
 

Explanation

There are 3 bags in total, and the total candies are 15. To distribute them equally, divide the candies evenly between the bags. Each bag will have 5 candies

Well explained 👍

Problem 2

A party has invites sent out in groups of 3, 5, and 15. How many should be sent to have equal groups?

Okay, lets begin

 Fifteen invitations are needed.
 

Explanation

Fifteen is the smallest number that can be divided by 3, 5, and 15 without leaving any extras. This makes it a perfect group size

Well explained 👍

Problem 3

3 kids jump after 3 seconds, 5 kids after 5 seconds, and 15 kids after 15 seconds, how long will they take to all jump at once?

Okay, lets begin

After 15 seconds, all the kids will jump together.
 

Explanation

 The jumping times match at 15 seconds because 15 is the smallest number that is a multiple of 3, 5, and 15.
 

Well explained 👍

Problem 4

A toy store has toys in sets of 3, 5, and 15. How many total toys for equal sets?

Okay, lets begin

There are 15 toys. You can make 3 sets of 5 toys each or 5 sets of 3 toys each.
 

Explanation

 You can divide 15 toys into equal sets in different ways, like making 3 sets with 5 toys or 5 sets with 3 toys.
 

Well explained 👍

Problem 5

Three friends play games in groups of 3, 5, and 15. How many total games until they play together?

Okay, lets begin

They will all play together after 15 games.
 

Explanation

The smallest number that 3, 5, and 15 all divide evenly into is 15. So, after 15 games, they will play together.
 

Well explained 👍

FAQs For LCM Of 3,5 and 15

1.What’s the LCM of 3,5 and 15?

The LCM is 15. In other words, 15 is the number we can divide by 3, 9, or 15, such that we end up with no remainder.
 

2.How is the LCM and GCF of 4, 10 and 20?

The GCF of 4, 10, and 20 is 2 because 2 is the greatest number that divides each of them. Their LCM is 20 because that is the least number they all multiply into.
 

3.Is the LCM of 3 and 5 also their HCF?

No, the LCM of 3 and 5 is 15, while their HCF (Highest Common Factor) is 1 since they have no common factors other than 1.
 

4.What is the prime factorization of 15?

 The prime factorization of 15 is 31 × 51. This means 15 is made up of the prime numbers 3 and 5 multiplied together.
 

Important Glossaries for LCM of 3,5 and 15

  • Least Common Multiple (LCM): The smallest number that can be evenly divided by two or more given numbers.
  • Prime Factorization: Breaking down a number into its prime factors, which are the prime numbers that multiply together to give the original number.
  • Prime Numbers: Numbers greater than 1 that have no positive divisors other than 1 and themselves (e.g., 2, 3, 5, 7).
  • Division Method: A technique for finding the LCM by dividing the given numbers by their prime factors until all are reduced to one.
     

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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

Fun Fact

: She loves to read number jokes and games.